Voronoi–Nasim summation formulas and index transforms

DOI10.1080/10652469.2011.595092zbMath1253.44007OpenAlexW2011917334MaRDI QIDQ2892832

Semyon B. Yakubovich

Publication date: 25 June 2012

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2011.595092

zbMATH Keywords

Mellin transformmodified Bessel functionsRiemann zeta-functionGauss hypergeometric functionKontorovich-Lebedev transformDirichlet divisor problemVoronoi summation formulaindex transformsFourier-Watson transformations

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Special integral transforms (Legendre, Hilbert, etc.) (44A15) (zeta (s)) and (L(s, chi)) (11M06) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Classical hypergeometric functions, ({}_2F_1) (33C05)

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New summation and transformation formulas of the Poisson, Müntz, Möbius and Voronoi type ⋮ A general class of Voronoi's and Koshliakov–Ramanujan's summation formulas involvingd_k(n)

Cites Work

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• On some relations which are equivalent to functional equations involving the Riemann zeta function
• \(L_p\)-boundedness of general index transforms
• General Transforms